Problem: Solve for $x$ : $6x^2 - 30x - 84 = 0$
Dividing both sides by $6$ gives: $ x^2 {-5}x {-14} = 0 $ The coefficient on the $x$ term is $-5$ and the constant term is $-14$ , so we need to find two numbers that add up to $-5$ and multiply to $-14$ The two numbers $2$ and $-7$ satisfy both conditions: $ {2} + {-7} = {-5} $ $ {2} \times {-7} = {-14} $ $(x + {2}) (x {-7}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 2) (x -7) = 0$ $x + 2 = 0$ or $x - 7 = 0$ Thus, $x = -2$ and $x = 7$ are the solutions.